Robot Kinematics Interpolation Using Local Support Points
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Solution Overview
Problem
The calculation of direct and indirect kinematics for robots is often demanding, particularly when an analytical solution is not possible, and requires both speed and accuracy, which existing methods struggle to achieve efficiently.
Innovation Solution
The method involves estimating kinematics based on local support points using spatial units and interpolation techniques, such as multilinear or barycentric interpolation, to determine configuration vectors or poses, allowing for faster and more accurate calculations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If analytical solution methods are used for kinematics calculation, then calculation accuracy is maintained, but calculation speed deteriorates and computational complexity increases
Solution Approach 1:
The work space is divided into multiple spatial units (e.g., voxels in 3D space), and pre-calculated configuration vectors are stored for discrete poses within each unit. This segmentation allows the system to quickly identify relevant pre-computed data without performing full analytical calculations for every query pose.
Solution Approach 2:
Configuration vectors for discrete poses at boundaries of spatial units are pre-calculated and stored in memory before runtime. When a target pose is queried, the system retrieves these pre-computed values and performs interpolation, avoiding the need for time-consuming analytical or iterative kinematics calculations during actual operation.
2Measurement precision
If iterative methods are used to improve calculation accuracy, then precision increases, but computation time increases and real-time control becomes difficult
Solution Approach 1:
Instead of performing iterative calculations to obtain accurate configuration vectors, the system creates a discrete copy of the kinematics data by pre-calculating configuration vectors at sampled poses and storing them. Runtime queries use interpolation on this discrete data copy, achieving high accuracy without iterative computation.
Solution Approach 2:
The system changes the parameter representation from continuous analytical functions to discrete sampled values with interpolation. By transforming the problem from solving differential equations or iterative optimizations to performing linear interpolations on pre-computed data, the computational complexity is dramatically reduced while maintaining accuracy.
3Measurement precision
If detailed spatial partitioning is used to improve interpolation accuracy, then kinematics estimation precision increases, but memory requirements and data structure complexity increase
Solution Approach 1:
The system extends the spatial partitioning into configuration space dimensions, creating a multi-dimensional grid structure where each spatial unit contains pre-computed configuration vectors. This dimensional extension allows the system to organize data in a structured manner that balances accuracy with manageable complexity through regular grid patterns.
Data Source
AI summary
A kinematic system is provided having a more efficient calculation of the direct and/or indirect kinematics. The direct/indirect kinematics of a kinematic system are estimated on the basis of local support points. In particular, when estimating the indirect kinematics, an interpolation is used which, for poses in a determined spatial unit, is based on predetermined configuration vectors which are each associated with a boundary point of the determined spatial unit in accordance with the indirect kinematics. When estimating the direct kinematics, an interpolation is used which, for configuration vectors in the determined spatial unit, is based on predetermined poses of the kinematic system which are each associated with a boundary point of the determined spatial unit in accordance with the direct kinematics.